Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process
The purpose of this study is to extend the idea of complex intuitionistic fuzzy set (CIFS) with a new notion referred to as a complex picture fuzzy set (CPFS). CPFS is a generalized version of CIFS since it includes a neutral membership degree in the concept. The capacity to cover a wider range of i...
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World Scientific Publishing
2024-01-01
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| Series: | Computing Open |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2972370124500089 |
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| author | Faisal Mehmood Heng Liu |
| author_facet | Faisal Mehmood Heng Liu |
| author_sort | Faisal Mehmood |
| collection | DOAJ |
| description | The purpose of this study is to extend the idea of complex intuitionistic fuzzy set (CIFS) with a new notion referred to as a complex picture fuzzy set (CPFS). CPFS is a generalized version of CIFS since it includes a neutral membership degree in the concept. The capacity to cover a wider range of information with the aid of neutral membership, non-membership, and membership makes this new theory distinctive. The unit disc of complex plane has been used to cover the range of values of membership degrees. Pertaining to Frank t-norm and t-conorm operations and a few aggregation methods, we establish some fundamental CPFS aggregation operators and attributes and use them to investigate multi-attribute decision-making (MADM) problems. Then, we offer various operators for the purpose of aggregating the CPF data. These are complex picture fuzzy Frank weighted averaging (CPFFWA), complex picture fuzzy Frank ordered weighted averaging (CPFFOWA), complex picture fuzzy Frank hybrid averaging (CPFFHA), and complex picture fuzzy Frank weighted geometric averaging (CPFFWGA), complex picture fuzzy Frank ordered weighted geometric averaging (CPFFOWG), and complex picture fuzzy frank hybrid geometric averaging (CPFFHGA) operators, which benefit from the basic Frank operations and averaging, geometric aggregation techniques. Furthermore, an algorithm for solving multi-attribute decision-making MADM problems has been presented under the framework of CPFSs by using CPFFWA and CPFFWG operators. Finally, in order to depict the potential applicability of our proposed technique, a numerical problem aiming at finding the best alternative has been solved and outcomes have been well compared with some existing techniques. |
| format | Article |
| id | doaj-art-5ec7950c444d4dd4af0ea913ced58832 |
| institution | Kabale University |
| issn | 2972-3701 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | World Scientific Publishing |
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| series | Computing Open |
| spelling | doaj-art-5ec7950c444d4dd4af0ea913ced588322025-02-04T03:24:11ZengWorld Scientific PublishingComputing Open2972-37012024-01-010210.1142/S2972370124500089Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) ProcessFaisal Mehmood0Heng Liu1School of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, P. R. ChinaSchool of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, P. R. ChinaThe purpose of this study is to extend the idea of complex intuitionistic fuzzy set (CIFS) with a new notion referred to as a complex picture fuzzy set (CPFS). CPFS is a generalized version of CIFS since it includes a neutral membership degree in the concept. The capacity to cover a wider range of information with the aid of neutral membership, non-membership, and membership makes this new theory distinctive. The unit disc of complex plane has been used to cover the range of values of membership degrees. Pertaining to Frank t-norm and t-conorm operations and a few aggregation methods, we establish some fundamental CPFS aggregation operators and attributes and use them to investigate multi-attribute decision-making (MADM) problems. Then, we offer various operators for the purpose of aggregating the CPF data. These are complex picture fuzzy Frank weighted averaging (CPFFWA), complex picture fuzzy Frank ordered weighted averaging (CPFFOWA), complex picture fuzzy Frank hybrid averaging (CPFFHA), and complex picture fuzzy Frank weighted geometric averaging (CPFFWGA), complex picture fuzzy Frank ordered weighted geometric averaging (CPFFOWG), and complex picture fuzzy frank hybrid geometric averaging (CPFFHGA) operators, which benefit from the basic Frank operations and averaging, geometric aggregation techniques. Furthermore, an algorithm for solving multi-attribute decision-making MADM problems has been presented under the framework of CPFSs by using CPFFWA and CPFFWG operators. Finally, in order to depict the potential applicability of our proposed technique, a numerical problem aiming at finding the best alternative has been solved and outcomes have been well compared with some existing techniques.https://www.worldscientific.com/doi/10.1142/S2972370124500089Complex picture fuzzy setFrank operationsaveraging operatorsgeometric operators |
| spellingShingle | Faisal Mehmood Heng Liu Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process Computing Open Complex picture fuzzy set Frank operations averaging operators geometric operators |
| title | Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process |
| title_full | Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process |
| title_fullStr | Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process |
| title_full_unstemmed | Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process |
| title_short | Some Complex Picture Fuzzy Aggregation Operators Based on Frank t-norm and t-conorm: An Application to Multi-Attribute Decision-Making (MADM) Process |
| title_sort | some complex picture fuzzy aggregation operators based on frank t norm and t conorm an application to multi attribute decision making madm process |
| topic | Complex picture fuzzy set Frank operations averaging operators geometric operators |
| url | https://www.worldscientific.com/doi/10.1142/S2972370124500089 |
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